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Simplifying 11t2 + -9t = 11 Reorder the terms: -9t + 11t2 = 11 Solving -9t + 11t2 = 11 Solving for variable 't'. Reorder the terms: -11 + -9t + 11t2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -9t + 11t2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1 + -0.8181818182t + t2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.8181818182t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + -0.8181818182t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.8181818182t + t2 = 0 + 1 -0.8181818182t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.8181818182t + t2 = 1 The t term is -0.8181818182t. Take half its coefficient (-0.4090909091). Square it (0.1673553719) and add it to both sides. Add '0.1673553719' to each side of the equation. -0.8181818182t + 0.1673553719 + t2 = 1 + 0.1673553719 Reorder the terms: 0.1673553719 + -0.8181818182t + t2 = 1 + 0.1673553719 Combine like terms: 1 + 0.1673553719 = 1.1673553719 0.1673553719 + -0.8181818182t + t2 = 1.1673553719 Factor a perfect square on the left side: (t + -0.4090909091)(t + -0.4090909091) = 1.1673553719 Calculate the square root of the right side: 1.080442211 Break this problem into two subproblems by setting (t + -0.4090909091) equal to 1.080442211 and -1.080442211.Subproblem 1
t + -0.4090909091 = 1.080442211 Simplifying t + -0.4090909091 = 1.080442211 Reorder the terms: -0.4090909091 + t = 1.080442211 Solving -0.4090909091 + t = 1.080442211 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4090909091' to each side of the equation. -0.4090909091 + 0.4090909091 + t = 1.080442211 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + t = 1.080442211 + 0.4090909091 t = 1.080442211 + 0.4090909091 Combine like terms: 1.080442211 + 0.4090909091 = 1.4895331201 t = 1.4895331201 Simplifying t = 1.4895331201Subproblem 2
t + -0.4090909091 = -1.080442211 Simplifying t + -0.4090909091 = -1.080442211 Reorder the terms: -0.4090909091 + t = -1.080442211 Solving -0.4090909091 + t = -1.080442211 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4090909091' to each side of the equation. -0.4090909091 + 0.4090909091 + t = -1.080442211 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + t = -1.080442211 + 0.4090909091 t = -1.080442211 + 0.4090909091 Combine like terms: -1.080442211 + 0.4090909091 = -0.6713513019 t = -0.6713513019 Simplifying t = -0.6713513019Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.4895331201, -0.6713513019}
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